On free Lie algebras and particles in electro-magnetic fields

Abstract

The Poincaré algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electro-magnetic backgrounds and possibly including the backreaction due the presence of multipoles. We point out a relation of this construction to free Lie algebras that gives a unified description of all possible kinematic extensions, leading to a symmetry algebra that we call Maxwell${}_{\infty }$. A specific dynamical system with this infinite symmetry is constructed and analysed.

1+27 pages. Mathematica notebook as ancillary file. v2: Added reference, JHEP version

References in corpus (3)

• Generalised Geometry for M-Theory
• Dynamics of Carroll Particles
• Superalgebras, constraints and partition functions

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• Hidden Role of Maxwell Superalgebras in the Free Differential Algebras of D=4 and D=11 Supergravity
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• Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions
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• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Exploring the geometry of supersymmetric double field theory
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Symmetries of M-theory and free Lie superalgebras
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• Extended Kinematical 3D Gravity Theories
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• Colourful Poincaré symmetry, gravity and particle actions
• Type II Double Field Theory in Superspace
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
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